The pilot stated that it was a very windy day with winds above 20 mph and gusts to 30 mph when he attempted a takeoff in his gyroplane. He stated that during the takeoff roll with the pre-rotor engaged to 130 to 140 RPM, he gently eased back on the cyclic and a gust of wind caught the rotors. He felt the rotor flap and then a bump. He immediately arrested the rotor flap and then continued the takeoff roll. When the gyroplane became airborne, he realized there was less rudder authority and returned to land at the departure airport without further incident. After landing, the pilot noticed that rudder had been damaged due to a rotor strike, which likely occurred when the rotor flapped during takeoff, resulting in substantial damage to the rudder. The pilot stated that he should have had the rotors pre-rotated to 160 RPM or greater prior to pulling back on the cyclic, and there were no preaccident mechanical malfunctions or failures of the gyroplane that would have precluded normal operation.